Score-based diffusion models for accurate crystal-structure inpainting and reconstruction of hydrogen positions

Generative artificial-intelligence (AI) models, such as score-based diffusion models, have recently advanced the field of computational materials science by enabling the generation of new materials with desired properties. In addition, these models could also be leveraged to reconstruct crystal structures for which partial information is available. One relevant example is the reliable determination of atomic positions occupied by hydrogen atoms in hydrogen-containing crystalline materials. While crucial to the analysis and prediction of many materials properties, the identification of hydrogen positions via X-ray scattering experiments has been historically challenging, and often requires more expensive neutron scattering measurements. As a consequence, and despite experimental advances which enable us nowadays to accurately determine hydrogen positions based on X-ray scattering experiments, inorganic crystallographic databases still report many lattice structures where hydrogen atoms have been either omitted or inserted with heuristics or by chemical intuition. Here, we combine diffusion models from the field of materials science with techniques originally developed in computer vision for image inpainting. We present how this knowledge transfer across domains enables a much faster and more accurate completion of host structures, compared to unconditioned diffusion models or previous approaches solely based on density-functional theory (DFT). Overall, when applied to a test dataset of hydrogen-containing materials from the MC3D database, our approach exceeds a success rate of 97% in terms of finding a structural match or predicting a more stable configuration (according to DFT) than the initial reference from the experimental source database (and with a success rate exceeding 99% when excluding structures flagged as theoretical in MC3D), both when starting from structures that were already relaxed with DFT, or when starting directly from the experimentally determined host structures.